with
\(\mathbf {\gamma } \triangleq [\gamma _1,\ldots ,\gamma _K]^T\)  being an auxiliary variable vector.
Unfortunately, optimization problem (REF ) is still intractable due to the complicated form of the sum of \(K\)  fractional terms. Next, we apply quadratic transform [1]} on the fractional terms to further transform them into solvable formula by introducing another auxiliary variable vector \(\mathbf {\tau }\triangleq [\tau _1,\ldots ,\tau _K]^T\) . Then the optimization problem (REF ) can be transformed into
\(\max _{\mathbf {w}_{k},\Phi _{\mathrm {r}},\Phi _{\mathrm {t}}, \mathbf {A}, \mathbf {\varsigma }, \mathbf {\gamma },\mathbf {\tau }} & h(\mathbf {\gamma }) + g(\mathbf {w}_{k},\Phi _{\mathrm {r}},\Phi _{\mathrm {t}}, \mathbf {A}, \mathbf {\varsigma }, \mathbf {\gamma },\mathbf {\tau })\\\mathrm {s.t.} ~~~~~&(\ref {eq:problem12})-(\ref {eq:problem16}),\) 
